LMFDB - Embedded newform 1110.2.h.d.961.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(961,1110)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1110.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.h (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{73})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 37x^{2} + 324 $ x^4 + 37*x^2 + 324
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			961.3
Root			$-3.77200i$ of defining polynomial
Character	$\chi$	$=$	1110.961
Dual form			1110.2.h.d.961.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.00000i q^{6} -1.00000 q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.00000i q^{6} -1.00000 q^{7} -1.00000i q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} -3.77200i q^{13} -1.00000i q^{14} +1.00000i q^{15} +1.00000 q^{16} -1.00000i q^{17} +1.00000i q^{18} +7.77200i q^{19} +1.00000i q^{20} +1.00000 q^{21} -1.00000i q^{22} +7.77200i q^{23} +1.00000i q^{24} -1.00000 q^{25} +3.77200 q^{26} -1.00000 q^{27} +1.00000 q^{28} +0.772002i q^{29} -1.00000 q^{30} +0.772002i q^{31} +1.00000i q^{32} +1.00000 q^{33} +1.00000 q^{34} +1.00000i q^{35} -1.00000 q^{36} +(4.77200 + 3.77200i) q^{37} -7.77200 q^{38} +3.77200i q^{39} -1.00000 q^{40} -0.772002 q^{41} +1.00000i q^{42} -1.22800i q^{43} +1.00000 q^{44} -1.00000i q^{45} -7.77200 q^{46} -1.00000 q^{48} -6.00000 q^{49} -1.00000i q^{50} +1.00000i q^{51} +3.77200i q^{52} -10.5440 q^{53} -1.00000i q^{54} +1.00000i q^{55} +1.00000i q^{56} -7.77200i q^{57} -0.772002 q^{58} +7.54400i q^{59} -1.00000i q^{60} +12.7720i q^{61} -0.772002 q^{62} -1.00000 q^{63} -1.00000 q^{64} -3.77200 q^{65} +1.00000i q^{66} +9.54400 q^{67} +1.00000i q^{68} -7.77200i q^{69} -1.00000 q^{70} -6.00000 q^{71} -1.00000i q^{72} +0.227998 q^{73} +(-3.77200 + 4.77200i) q^{74} +1.00000 q^{75} -7.77200i q^{76} +1.00000 q^{77} -3.77200 q^{78} +11.5440i q^{79} -1.00000i q^{80} +1.00000 q^{81} -0.772002i q^{82} -1.77200 q^{83} -1.00000 q^{84} -1.00000 q^{85} +1.22800 q^{86} -0.772002i q^{87} +1.00000i q^{88} +17.3160i q^{89} +1.00000 q^{90} +3.77200i q^{91} -7.77200i q^{92} -0.772002i q^{93} +7.77200 q^{95} -1.00000i q^{96} +10.7720i q^{97} -6.00000i q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} - 4 q^{4} - 4 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 - 4 * q^4 - 4 * q^7 + 4 * q^9	$ 4 q - 4 q^{3} - 4 q^{4} - 4 q^{7} + 4 q^{9} + 4 q^{10} - 4 q^{11} + 4 q^{12} + 4 q^{16} + 4 q^{21} - 4 q^{25} - 2 q^{26} - 4 q^{27} + 4 q^{28} - 4 q^{30} + 4 q^{33} + 4 q^{34} - 4 q^{36} + 2 q^{37} - 14 q^{38} - 4 q^{40} + 14 q^{41} + 4 q^{44} - 14 q^{46} - 4 q^{48} - 24 q^{49} - 8 q^{53} + 14 q^{58} + 14 q^{62} - 4 q^{63} - 4 q^{64} + 2 q^{65} + 4 q^{67} - 4 q^{70} - 24 q^{71} + 18 q^{73} + 2 q^{74} + 4 q^{75} + 4 q^{77} + 2 q^{78} + 4 q^{81} + 10 q^{83} - 4 q^{84} - 4 q^{85} + 22 q^{86} + 4 q^{90} + 14 q^{95} - 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 - 4 * q^4 - 4 * q^7 + 4 * q^9 + 4 * q^10 - 4 * q^11 + 4 * q^12 + 4 * q^16 + 4 * q^21 - 4 * q^25 - 2 * q^26 - 4 * q^27 + 4 * q^28 - 4 * q^30 + 4 * q^33 + 4 * q^34 - 4 * q^36 + 2 * q^37 - 14 * q^38 - 4 * q^40 + 14 * q^41 + 4 * q^44 - 14 * q^46 - 4 * q^48 - 24 * q^49 - 8 * q^53 + 14 * q^58 + 14 * q^62 - 4 * q^63 - 4 * q^64 + 2 * q^65 + 4 * q^67 - 4 * q^70 - 24 * q^71 + 18 * q^73 + 2 * q^74 + 4 * q^75 + 4 * q^77 + 2 * q^78 + 4 * q^81 + 10 * q^83 - 4 * q^84 - 4 * q^85 + 22 * q^86 + 4 * q^90 + 14 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.00000			−0.500000
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		−	1.00000i		−	0.408248i
$7$	−1.00000			−0.377964			−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000			−0.377964			−0.188982	+	0.981981i	$0.560519\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.00000			0.333333
$10$	1.00000			0.316228
$11$	−1.00000			−0.301511			−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000			−0.301511			−0.150756	+	0.988571i	$0.548171\pi$
$12$	1.00000			0.288675
$13$		−	3.77200i		−	1.04617i	−0.852282	−	0.523083i	$-0.824782\pi$
$13$		−	3.77200i		−	1.04617i	0.852282	−	0.523083i	$-0.175218\pi$
$14$		−	1.00000i		−	0.267261i
$15$			1.00000i			0.258199i
$16$	1.00000			0.250000
$17$		−	1.00000i		−	0.242536i	−0.992620	−	0.121268i	$-0.961304\pi$
$17$		−	1.00000i		−	0.242536i	0.992620	−	0.121268i	$-0.0386960\pi$
$18$			1.00000i			0.235702i
$19$			7.77200i			1.78302i	0.453001	+	0.891510i	$0.350353\pi$
$19$			7.77200i			1.78302i	−0.453001	+	0.891510i	$0.649647\pi$
$20$			1.00000i			0.223607i
$21$	1.00000			0.218218
$22$		−	1.00000i		−	0.213201i
$23$			7.77200i			1.62057i	0.586033	+	0.810287i	$0.300689\pi$
$23$			7.77200i			1.62057i	−0.586033	+	0.810287i	$0.699311\pi$
$24$			1.00000i			0.204124i
$25$	−1.00000			−0.200000
$26$	3.77200			0.739750
$27$	−1.00000			−0.192450
$28$	1.00000			0.188982
$29$			0.772002i			0.143357i	0.997428	+	0.0716786i	$0.0228356\pi$
$29$			0.772002i			0.143357i	−0.997428	+	0.0716786i	$0.977164\pi$
$30$	−1.00000			−0.182574
$31$			0.772002i			0.138656i	0.997594	+	0.0693278i	$0.0220854\pi$
$31$			0.772002i			0.138656i	−0.997594	+	0.0693278i	$0.977915\pi$
$32$			1.00000i			0.176777i
$33$	1.00000			0.174078
$34$	1.00000			0.171499
$35$			1.00000i			0.169031i
$36$	−1.00000			−0.166667
$37$	4.77200	+	3.77200i	0.784512	+	0.620113i
$37$	4.77200	+	3.77200i	0.784512	+	0.620113i
$38$	−7.77200			−1.26079
$39$			3.77200i			0.604004i
$40$	−1.00000			−0.158114
$41$	−0.772002			−0.120566			−0.0602832	−	0.998181i	$-0.519200\pi$
$41$	−0.772002			−0.120566			−0.0602832	+	0.998181i	$0.519200\pi$
$42$			1.00000i			0.154303i
$43$		−	1.22800i		−	0.187268i	−0.995607	−	0.0936340i	$-0.970152\pi$
$43$		−	1.22800i		−	0.187268i	0.995607	−	0.0936340i	$-0.0298483\pi$
$44$	1.00000			0.150756
$45$		−	1.00000i		−	0.149071i
$46$	−7.77200			−1.14592
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	−1.00000			−0.144338
$49$	−6.00000			−0.857143
$50$		−	1.00000i		−	0.141421i
$51$			1.00000i			0.140028i
$52$			3.77200i			0.523083i
$53$	−10.5440			−1.44833			−0.724165	−	0.689627i	$-0.757775\pi$
$53$	−10.5440			−1.44833			−0.724165	+	0.689627i	$0.757775\pi$
$54$		−	1.00000i		−	0.136083i
$55$			1.00000i			0.134840i
$56$			1.00000i			0.133631i
$57$		−	7.77200i		−	1.02943i
$58$	−0.772002			−0.101369
$59$			7.54400i			0.982146i	0.871119	+	0.491073i	$0.163395\pi$
$59$			7.54400i			0.982146i	−0.871119	+	0.491073i	$0.836605\pi$
$60$		−	1.00000i		−	0.129099i
$61$			12.7720i			1.63529i	0.575725	+	0.817644i	$0.304720\pi$
$61$			12.7720i			1.63529i	−0.575725	+	0.817644i	$0.695280\pi$
$62$	−0.772002			−0.0980443
$63$	−1.00000			−0.125988
$64$	−1.00000			−0.125000
$65$	−3.77200			−0.467859
$66$			1.00000i			0.123091i
$67$	9.54400			1.16599			0.582993	−	0.812477i	$-0.301882\pi$
$67$	9.54400			1.16599			0.582993	+	0.812477i	$0.301882\pi$
$68$			1.00000i			0.121268i
$69$		−	7.77200i		−	0.935639i
$70$	−1.00000			−0.119523
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		−	1.00000i		−	0.117851i
$73$	0.227998			0.0266852			0.0133426	−	0.999911i	$-0.495753\pi$
$73$	0.227998			0.0266852			0.0133426	+	0.999911i	$0.495753\pi$
$74$	−3.77200	+	4.77200i	−0.438486	+	0.554734i
$75$	1.00000			0.115470
$76$		−	7.77200i		−	0.891510i
$77$	1.00000			0.113961
$78$	−3.77200			−0.427095
$79$			11.5440i			1.29880i	0.760446	+	0.649401i	$0.224980\pi$
$79$			11.5440i			1.29880i	−0.760446	+	0.649401i	$0.775020\pi$
$80$		−	1.00000i		−	0.111803i
$81$	1.00000			0.111111
$82$		−	0.772002i		−	0.0852533i
$83$	−1.77200			−0.194502			−0.0972512	−	0.995260i	$-0.531005\pi$
$83$	−1.77200			−0.194502			−0.0972512	+	0.995260i	$0.531005\pi$
$84$	−1.00000			−0.109109
$85$	−1.00000			−0.108465
$86$	1.22800			0.132418
$87$		−	0.772002i		−	0.0827673i
$88$			1.00000i			0.106600i
$89$			17.3160i			1.83549i	0.397167	+	0.917746i	$0.369993\pi$
$89$			17.3160i			1.83549i	−0.397167	+	0.917746i	$0.630007\pi$
$90$	1.00000			0.105409
$91$			3.77200i			0.395413i
$92$		−	7.77200i		−	0.810287i
$93$		−	0.772002i		−	0.0800529i
$94$		0			0
$95$	7.77200			0.797391
$96$		−	1.00000i		−	0.102062i
$97$			10.7720i			1.09373i	0.837220	+	0.546866i	$0.184179\pi$
$97$			10.7720i			1.09373i	−0.837220	+	0.546866i	$0.815821\pi$
$98$		−	6.00000i		−	0.606092i
$99$	−1.00000			−0.100504
$100$	1.00000			0.100000
$101$	−11.5440			−1.14867			−0.574336	−	0.818620i	$-0.694740\pi$
$101$	−11.5440			−1.14867			−0.574336	+	0.818620i	$0.694740\pi$
$102$	−1.00000			−0.0990148
$103$		−	17.5440i		−	1.72866i	−0.502923	−	0.864331i	$-0.667742\pi$
$103$		−	17.5440i		−	1.72866i	0.502923	−	0.864331i	$-0.332258\pi$
$104$	−3.77200			−0.369875
$105$		−	1.00000i		−	0.0975900i
$106$		−	10.5440i		−	1.02412i
$107$	−7.77200			−0.751348			−0.375674	−	0.926752i	$-0.622589\pi$
$107$	−7.77200			−0.751348			−0.375674	+	0.926752i	$0.622589\pi$
$108$	1.00000			0.0962250
$109$		−	7.00000i		−	0.670478i	−0.942133	−	0.335239i	$-0.891183\pi$
$109$		−	7.00000i		−	0.670478i	0.942133	−	0.335239i	$-0.108817\pi$
$110$	−1.00000			−0.0953463
$111$	−4.77200	−	3.77200i	−0.452938	−	0.358023i
$112$	−1.00000			−0.0944911
$113$		−	14.3160i		−	1.34674i	−0.739307	−	0.673368i	$-0.764847\pi$
$113$		−	14.3160i		−	1.34674i	0.739307	−	0.673368i	$-0.235153\pi$
$114$	7.77200			0.727915
$115$	7.77200			0.724743
$116$		−	0.772002i		−	0.0716786i
$117$		−	3.77200i		−	0.348722i
$118$	−7.54400			−0.694482
$119$			1.00000i			0.0916698i
$120$	1.00000			0.0912871
$121$	−10.0000			−0.909091
$122$	−12.7720			−1.15632
$123$	0.772002			0.0696091
$124$		−	0.772002i		−	0.0693278i
$125$			1.00000i			0.0894427i
$126$		−	1.00000i		−	0.0890871i
$127$	13.3160			1.18160			0.590802	−	0.806816i	$-0.298811\pi$
$127$	13.3160			1.18160			0.590802	+	0.806816i	$0.298811\pi$
$128$		−	1.00000i		−	0.0883883i
$129$			1.22800i			0.108119i
$130$		−	3.77200i		−	0.330826i
$131$		−	0.455996i		−	0.0398406i	−0.999802	−	0.0199203i	$-0.993659\pi$
$131$		−	0.455996i		−	0.0398406i	0.999802	−	0.0199203i	$-0.00634124\pi$
$132$	−1.00000			−0.0870388
$133$		−	7.77200i		−	0.673918i
$134$			9.54400i			0.824476i
$135$			1.00000i			0.0860663i
$136$	−1.00000			−0.0857493
$137$	−19.0880			−1.63080			−0.815399	−	0.578899i	$-0.803483\pi$
$137$	−19.0880			−1.63080			−0.815399	+	0.578899i	$0.803483\pi$
$138$	7.77200			0.661597
$139$	20.3160			1.72318			0.861591	−	0.507604i	$-0.169469\pi$
$139$	20.3160			1.72318			0.861591	+	0.507604i	$0.169469\pi$
$140$		−	1.00000i		−	0.0845154i
$141$		0			0
$142$		−	6.00000i		−	0.503509i
$143$			3.77200i			0.315431i
$144$	1.00000			0.0833333
$145$	0.772002			0.0641113
$146$			0.227998i			0.0188693i
$147$	6.00000			0.494872
$148$	−4.77200	−	3.77200i	−0.392256	−	0.310057i
$149$	−6.00000			−0.491539			−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000			−0.491539			−0.245770	+	0.969328i	$0.579041\pi$
$150$			1.00000i			0.0816497i
$151$	8.22800			0.669585			0.334792	−	0.942292i	$-0.391334\pi$
$151$	8.22800			0.669585			0.334792	+	0.942292i	$0.391334\pi$
$152$	7.77200			0.630393
$153$		−	1.00000i		−	0.0808452i
$154$			1.00000i			0.0805823i
$155$	0.772002			0.0620087
$156$		−	3.77200i		−	0.302002i
$157$	17.8600			1.42538			0.712692	−	0.701477i	$-0.247476\pi$
$157$	17.8600			1.42538			0.712692	+	0.701477i	$0.247476\pi$
$158$	−11.5440			−0.918392
$159$	10.5440			0.836194
$160$	1.00000			0.0790569
$161$		−	7.77200i		−	0.612520i
$162$			1.00000i			0.0785674i
$163$			3.45600i			0.270695i	0.990798	+	0.135347i	$0.0432150\pi$
$163$			3.45600i			0.270695i	−0.990798	+	0.135347i	$0.956785\pi$
$164$	0.772002			0.0602832
$165$		−	1.00000i		−	0.0778499i
$166$		−	1.77200i		−	0.137534i
$167$			11.3160i			0.875659i	0.899058	+	0.437829i	$0.144253\pi$
$167$			11.3160i			0.875659i	−0.899058	+	0.437829i	$0.855747\pi$
$168$		−	1.00000i		−	0.0771517i
$169$	−1.22800			−0.0944614
$170$		−	1.00000i		−	0.0766965i
$171$			7.77200i			0.594340i
$172$			1.22800i			0.0936340i
$173$	15.0000			1.14043			0.570214	−	0.821496i	$-0.306860\pi$
$173$	15.0000			1.14043			0.570214	+	0.821496i	$0.306860\pi$
$174$	0.772002			0.0585253
$175$	1.00000			0.0755929
$176$	−1.00000			−0.0753778
$177$		−	7.54400i		−	0.567042i
$178$	−17.3160			−1.29789
$179$			9.54400i			0.713352i	0.934228	+	0.356676i	$0.116090\pi$
$179$			9.54400i			0.713352i	−0.934228	+	0.356676i	$0.883910\pi$
$180$			1.00000i			0.0745356i
$181$	23.5440			1.75001			0.875006	−	0.484112i	$-0.160857\pi$
$181$	23.5440			1.75001			0.875006	+	0.484112i	$0.160857\pi$
$182$	−3.77200			−0.279599
$183$		−	12.7720i		−	0.944134i
$184$	7.77200			0.572960
$185$	3.77200	−	4.77200i	0.277323	−	0.350845i
$186$	0.772002			0.0566059
$187$			1.00000i			0.0731272i
$188$		0			0
$189$	1.00000			0.0727393
$190$			7.77200i			0.563840i
$191$		−	12.5440i		−	0.907652i	−0.891090	−	0.453826i	$-0.850059\pi$
$191$		−	12.5440i		−	0.907652i	0.891090	−	0.453826i	$-0.149941\pi$
$192$	1.00000			0.0721688
$193$			6.45600i			0.464713i	0.972631	+	0.232356i	$0.0746436\pi$
$193$			6.45600i			0.464713i	−0.972631	+	0.232356i	$0.925356\pi$
$194$	−10.7720			−0.773385
$195$	3.77200			0.270119
$196$	6.00000			0.428571
$197$	11.7720			0.838720			0.419360	−	0.907820i	$-0.362254\pi$
$197$	11.7720			0.838720			0.419360	+	0.907820i	$0.362254\pi$
$198$		−	1.00000i		−	0.0710669i
$199$			7.54400i			0.534780i	0.963588	+	0.267390i	$0.0861612\pi$
$199$			7.54400i			0.534780i	−0.963588	+	0.267390i	$0.913839\pi$
$200$			1.00000i			0.0707107i
$201$	−9.54400			−0.673182
$202$		−	11.5440i		−	0.812233i
$203$		−	0.772002i		−	0.0541839i
$204$		−	1.00000i		−	0.0700140i
$205$			0.772002i			0.0539189i
$206$	17.5440			1.22235
$207$			7.77200i			0.540191i
$208$		−	3.77200i		−	0.261541i
$209$		−	7.77200i		−	0.537601i
$210$	1.00000			0.0690066
$211$	−11.2280			−0.772967			−0.386484	−	0.922296i	$-0.626310\pi$
$211$	−11.2280			−0.772967			−0.386484	+	0.922296i	$0.626310\pi$
$212$	10.5440			0.724165
$213$	6.00000			0.411113
$214$		−	7.77200i		−	0.531283i
$215$	−1.22800			−0.0837488
$216$			1.00000i			0.0680414i
$217$		−	0.772002i		−	0.0524069i
$218$	7.00000			0.474100
$219$	−0.227998			−0.0154067
$220$		−	1.00000i		−	0.0674200i
$221$	−3.77200			−0.253732
$222$	3.77200	−	4.77200i	0.253160	−	0.320276i
$223$	−17.2280			−1.15367			−0.576836	−	0.816860i	$-0.695713\pi$
$223$	−17.2280			−1.15367			−0.576836	+	0.816860i	$0.695713\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	−1.00000			−0.0666667
$226$	14.3160			0.952287
$227$		−	6.77200i		−	0.449474i	−0.974420	−	0.224737i	$-0.927848\pi$
$227$		−	6.77200i		−	0.449474i	0.974420	−	0.224737i	$-0.0721522\pi$
$228$			7.77200i			0.514713i
$229$	13.5440			0.895013			0.447506	−	0.894281i	$-0.352312\pi$
$229$	13.5440			0.895013			0.447506	+	0.894281i	$0.352312\pi$
$230$			7.77200i			0.512471i
$231$	−1.00000			−0.0657952
$232$	0.772002			0.0506844
$233$	−12.0000			−0.786146			−0.393073	−	0.919507i	$-0.628588\pi$
$233$	−12.0000			−0.786146			−0.393073	+	0.919507i	$0.628588\pi$
$234$	3.77200			0.246583
$235$		0			0
$236$		−	7.54400i		−	0.491073i
$237$		−	11.5440i		−	0.749864i
$238$	−1.00000			−0.0648204
$239$			5.22800i			0.338171i	0.985601	+	0.169086i	$0.0540814\pi$
$239$			5.22800i			0.338171i	−0.985601	+	0.169086i	$0.945919\pi$
$240$			1.00000i			0.0645497i
$241$		−	16.0000i		−	1.03065i	−0.856995	−	0.515325i	$-0.827671\pi$
$241$		−	16.0000i		−	1.03065i	0.856995	−	0.515325i	$-0.172329\pi$
$242$		−	10.0000i		−	0.642824i
$243$	−1.00000			−0.0641500
$244$		−	12.7720i		−	0.817644i
$245$			6.00000i			0.383326i
$246$			0.772002i			0.0492210i
$247$	29.3160			1.86533
$248$	0.772002			0.0490222
$249$	1.77200			0.112296
$250$	−1.00000			−0.0632456
$251$			27.0880i			1.70978i	0.518809	+	0.854890i	$0.326375\pi$
$251$			27.0880i			1.70978i	−0.518809	+	0.854890i	$0.673625\pi$
$252$	1.00000			0.0629941
$253$		−	7.77200i		−	0.488622i
$254$			13.3160i			0.835521i
$255$	1.00000			0.0626224
$256$	1.00000			0.0625000
$257$			4.22800i			0.263735i	0.991267	+	0.131868i	$0.0420974\pi$
$257$			4.22800i			0.263735i	−0.991267	+	0.131868i	$0.957903\pi$
$258$	−1.22800			−0.0764518
$259$	−4.77200	−	3.77200i	−0.296518	−	0.234381i
$260$	3.77200			0.233930
$261$			0.772002i			0.0477857i
$262$	0.455996			0.0281715
$263$	5.22800			0.322372			0.161186	−	0.986924i	$-0.448468\pi$
$263$	5.22800			0.322372			0.161186	+	0.986924i	$0.448468\pi$
$264$		−	1.00000i		−	0.0615457i
$265$			10.5440i			0.647713i
$266$	7.77200			0.476532
$267$		−	17.3160i		−	1.05972i
$268$	−9.54400			−0.582993
$269$	9.31601			0.568007			0.284003	−	0.958823i	$-0.408337\pi$
$269$	9.31601			0.568007			0.284003	+	0.958823i	$0.408337\pi$
$270$	−1.00000			−0.0608581
$271$	−23.0880			−1.40250			−0.701248	−	0.712917i	$-0.747374\pi$
$271$	−23.0880			−1.40250			−0.701248	+	0.712917i	$0.747374\pi$
$272$		−	1.00000i		−	0.0606339i
$273$		−	3.77200i		−	0.228292i
$274$		−	19.0880i		−	1.15315i
$275$	1.00000			0.0603023
$276$			7.77200i			0.467820i
$277$		−	6.22800i		−	0.374204i	−0.982340	−	0.187102i	$-0.940090\pi$
$277$		−	6.22800i		−	0.374204i	0.982340	−	0.187102i	$-0.0599095\pi$
$278$			20.3160i			1.21847i
$279$			0.772002i			0.0462185i
$280$	1.00000			0.0597614
$281$		−	3.77200i		−	0.225019i	−0.993651	−	0.112509i	$-0.964111\pi$
$281$		−	3.77200i		−	0.225019i	0.993651	−	0.112509i	$-0.0358888\pi$
$282$		0			0
$283$			2.22800i			0.132441i	0.997805	+	0.0662204i	$0.0210940\pi$
$283$			2.22800i			0.132441i	−0.997805	+	0.0662204i	$0.978906\pi$
$284$	6.00000			0.356034
$285$	−7.77200			−0.460374
$286$	−3.77200			−0.223043
$287$	0.772002			0.0455698
$288$			1.00000i			0.0589256i
$289$	16.0000			0.941176
$290$			0.772002i			0.0453335i
$291$		−	10.7720i		−	0.631466i
$292$	−0.227998			−0.0133426
$293$	−9.00000			−0.525786			−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000			−0.525786			−0.262893	+	0.964825i	$0.584677\pi$
$294$			6.00000i			0.349927i
$295$	7.54400			0.439229
$296$	3.77200	−	4.77200i	0.219243	−	0.277367i
$297$	1.00000			0.0580259
$298$		−	6.00000i		−	0.347571i
$299$	29.3160			1.69539
$300$	−1.00000			−0.0577350
$301$			1.22800i			0.0707806i
$302$			8.22800i			0.473468i
$303$	11.5440			0.663186
$304$			7.77200i			0.445755i
$305$	12.7720			0.731323
$306$	1.00000			0.0571662
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	−1.00000			−0.0569803
$309$			17.5440i			0.998044i
$310$			0.772002i			0.0438468i
$311$			6.77200i			0.384005i	0.981394	+	0.192002i	$0.0614982\pi$
$311$			6.77200i			0.384005i	−0.981394	+	0.192002i	$0.938502\pi$
$312$	3.77200			0.213548
$313$		−	17.0880i		−	0.965871i	−0.875656	−	0.482936i	$-0.839571\pi$
$313$		−	17.0880i		−	0.965871i	0.875656	−	0.482936i	$-0.160429\pi$
$314$			17.8600i			1.00790i
$315$			1.00000i			0.0563436i
$316$		−	11.5440i		−	0.649401i
$317$	−33.4040			−1.87616			−0.938078	−	0.346424i	$-0.887396\pi$
$317$	−33.4040			−1.87616			−0.938078	+	0.346424i	$0.887396\pi$
$318$			10.5440i			0.591278i
$319$		−	0.772002i		−	0.0432238i
$320$			1.00000i			0.0559017i
$321$	7.77200			0.433791
$322$	7.77200			0.433117
$323$	7.77200			0.432446
$324$	−1.00000			−0.0555556
$325$			3.77200i			0.209233i
$326$	−3.45600			−0.191410
$327$			7.00000i			0.387101i
$328$			0.772002i			0.0426267i
$329$		0			0
$330$	1.00000			0.0550482
$331$			17.5440i			0.964306i	0.876087	+	0.482153i	$0.160145\pi$
$331$			17.5440i			0.964306i	−0.876087	+	0.482153i	$0.839855\pi$
$332$	1.77200			0.0972512
$333$	4.77200	+	3.77200i	0.261504	+	0.206704i
$334$	−11.3160			−0.619184
$335$		−	9.54400i		−	0.521445i
$336$	1.00000			0.0545545
$337$	−1.31601			−0.0716874			−0.0358437	−	0.999357i	$-0.511412\pi$
$337$	−1.31601			−0.0716874			−0.0358437	+	0.999357i	$0.511412\pi$
$338$		−	1.22800i		−	0.0667943i
$339$			14.3160i			0.777539i
$340$	1.00000			0.0542326
$341$		−	0.772002i		−	0.0418062i
$342$	−7.77200			−0.420262
$343$	13.0000			0.701934
$344$	−1.22800			−0.0662092
$345$	−7.77200			−0.418431
$346$			15.0000i			0.806405i
$347$		−	23.5440i		−	1.26391i	−0.775006	−	0.631954i	$-0.782253\pi$
$347$		−	23.5440i		−	1.26391i	0.775006	−	0.631954i	$-0.217747\pi$
$348$			0.772002i			0.0413836i
$349$	−6.00000			−0.321173			−0.160586	−	0.987022i	$-0.551338\pi$
$349$	−6.00000			−0.321173			−0.160586	+	0.987022i	$0.551338\pi$
$350$			1.00000i			0.0534522i
$351$			3.77200i			0.201335i
$352$		−	1.00000i		−	0.0533002i
$353$		−	36.7720i		−	1.95718i	−0.205828	−	0.978588i	$-0.565989\pi$
$353$		−	36.7720i		−	1.95718i	0.205828	−	0.978588i	$-0.434011\pi$
$354$	7.54400			0.400959
$355$			6.00000i			0.318447i
$356$		−	17.3160i		−	0.917746i
$357$		−	1.00000i		−	0.0529256i
$358$	−9.54400			−0.504416
$359$	−4.45600			−0.235178			−0.117589	−	0.993062i	$-0.537517\pi$
$359$	−4.45600			−0.235178			−0.117589	+	0.993062i	$0.537517\pi$
$360$	−1.00000			−0.0527046
$361$	−41.4040			−2.17916
$362$			23.5440i			1.23745i
$363$	10.0000			0.524864
$364$		−	3.77200i		−	0.197707i
$365$		−	0.227998i		−	0.0119340i
$366$	12.7720			0.667603
$367$	−16.0880			−0.839787			−0.419894	−	0.907573i	$-0.637933\pi$
$367$	−16.0880			−0.839787			−0.419894	+	0.907573i	$0.637933\pi$
$368$			7.77200i			0.405144i
$369$	−0.772002			−0.0401888
$370$	4.77200	+	3.77200i	0.248085	+	0.196097i
$371$	10.5440			0.547417
$372$			0.772002i			0.0400264i
$373$	21.5440			1.11551			0.557753	−	0.830007i	$-0.311664\pi$
$373$	21.5440			1.11551			0.557753	+	0.830007i	$0.311664\pi$
$374$	−1.00000			−0.0517088
$375$		−	1.00000i		−	0.0516398i
$376$		0			0
$377$	2.91199			0.149975
$378$			1.00000i			0.0514344i
$379$	−23.5440			−1.20937			−0.604687	−	0.796463i	$-0.706702\pi$
$379$	−23.5440			−1.20937			−0.604687	+	0.796463i	$0.706702\pi$
$380$	−7.77200			−0.398695
$381$	−13.3160			−0.682200
$382$	12.5440			0.641807
$383$			15.3160i			0.782611i	0.920261	+	0.391306i	$0.127976\pi$
$383$			15.3160i			0.782611i	−0.920261	+	0.391306i	$0.872024\pi$
$384$			1.00000i			0.0510310i
$385$		−	1.00000i		−	0.0509647i
$386$	−6.45600			−0.328602
$387$		−	1.22800i		−	0.0624227i
$388$		−	10.7720i		−	0.546866i
$389$		−	6.77200i		−	0.343354i	−0.985153	−	0.171677i	$-0.945081\pi$
$389$		−	6.77200i		−	0.343354i	0.985153	−	0.171677i	$-0.0549186\pi$
$390$			3.77200i			0.191003i
$391$	7.77200			0.393047
$392$			6.00000i			0.303046i
$393$			0.455996i			0.0230020i
$394$			11.7720i			0.593065i
$395$	11.5440			0.580842
$396$	1.00000			0.0502519
$397$	1.54400			0.0774913			0.0387457	−	0.999249i	$-0.487664\pi$
$397$	1.54400			0.0774913			0.0387457	+	0.999249i	$0.487664\pi$
$398$	−7.54400			−0.378147
$399$			7.77200i			0.389087i
$400$	−1.00000			−0.0500000
$401$		−	23.3160i		−	1.16435i	−0.813065	−	0.582173i	$-0.802203\pi$
$401$		−	23.3160i		−	1.16435i	0.813065	−	0.582173i	$-0.197797\pi$
$402$		−	9.54400i		−	0.476012i
$403$	2.91199			0.145057
$404$	11.5440			0.574336
$405$		−	1.00000i		−	0.0496904i
$406$	0.772002			0.0383138
$407$	−4.77200	−	3.77200i	−0.236539	−	0.186971i
$408$	1.00000			0.0495074
$409$		−	4.00000i		−	0.197787i	−0.995098	−	0.0988936i	$-0.968470\pi$
$409$		−	4.00000i		−	0.197787i	0.995098	−	0.0988936i	$-0.0315304\pi$
$410$	−0.772002			−0.0381265
$411$	19.0880			0.941542
$412$			17.5440i			0.864331i
$413$		−	7.54400i		−	0.371216i
$414$	−7.77200			−0.381973
$415$			1.77200i			0.0869842i
$416$	3.77200			0.184938
$417$	−20.3160			−0.994879
$418$	7.77200			0.380141
$419$	12.8600			0.628253			0.314126	−	0.949381i	$-0.398288\pi$
$419$	12.8600			0.628253			0.314126	+	0.949381i	$0.398288\pi$
$420$			1.00000i			0.0487950i
$421$			6.00000i			0.292422i	0.989253	+	0.146211i	$0.0467079\pi$
$421$			6.00000i			0.292422i	−0.989253	+	0.146211i	$0.953292\pi$
$422$		−	11.2280i		−	0.546570i
$423$		0			0
$424$			10.5440i			0.512062i
$425$			1.00000i			0.0485071i
$426$			6.00000i			0.290701i
$427$		−	12.7720i		−	0.618080i
$428$	7.77200			0.375674
$429$		−	3.77200i		−	0.182114i
$430$		−	1.22800i		−	0.0592193i
$431$		−	10.0880i		−	0.485922i	−0.970036	−	0.242961i	$-0.921881\pi$
$431$		−	10.0880i		−	0.485922i	0.970036	−	0.242961i	$-0.0781187\pi$
$432$	−1.00000			−0.0481125
$433$	−7.77200			−0.373499			−0.186749	−	0.982408i	$-0.559795\pi$
$433$	−7.77200			−0.373499			−0.186749	+	0.982408i	$0.559795\pi$
$434$	0.772002			0.0370573
$435$	−0.772002			−0.0370147
$436$			7.00000i			0.335239i
$437$	−60.4040			−2.88952
$438$		−	0.227998i		−	0.0108942i
$439$		−	20.7720i		−	0.991394i	−0.868496	−	0.495697i	$-0.834913\pi$
$439$		−	20.7720i		−	0.991394i	0.868496	−	0.495697i	$-0.165087\pi$
$440$	1.00000			0.0476731
$441$	−6.00000			−0.285714
$442$		−	3.77200i		−	0.179416i
$443$	−20.0000			−0.950229			−0.475114	−	0.879924i	$-0.657593\pi$
$443$	−20.0000			−0.950229			−0.475114	+	0.879924i	$0.657593\pi$
$444$	4.77200	+	3.77200i	0.226469	+	0.179011i
$445$	17.3160			0.820857
$446$		−	17.2280i		−	0.815769i
$447$	6.00000			0.283790
$448$	1.00000			0.0472456
$449$			2.00000i			0.0943858i	0.998886	+	0.0471929i	$0.0150276\pi$
$449$			2.00000i			0.0943858i	−0.998886	+	0.0471929i	$0.984972\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	0.772002			0.0363521
$452$			14.3160i			0.673368i
$453$	−8.22800			−0.386585
$454$	6.77200			0.317826
$455$	3.77200			0.176834
$456$	−7.77200			−0.363957
$457$			34.3160i			1.60524i	0.596494	+	0.802618i	$0.296560\pi$
$457$			34.3160i			1.60524i	−0.596494	+	0.802618i	$0.703440\pi$
$458$			13.5440i			0.632870i
$459$			1.00000i			0.0466760i
$460$	−7.77200			−0.362371
$461$			21.2280i			0.988686i	0.869267	+	0.494343i	$0.164591\pi$
$461$			21.2280i			0.988686i	−0.869267	+	0.494343i	$0.835409\pi$
$462$		−	1.00000i		−	0.0465242i
$463$		−	30.6320i		−	1.42359i	−0.702387	−	0.711795i	$-0.747882\pi$
$463$		−	30.6320i		−	1.42359i	0.702387	−	0.711795i	$-0.252118\pi$
$464$			0.772002i			0.0358393i
$465$	−0.772002			−0.0358007
$466$		−	12.0000i		−	0.555889i
$467$		−	4.31601i		−	0.199721i	−0.995001	−	0.0998605i	$-0.968160\pi$
$467$		−	4.31601i		−	0.199721i	0.995001	−	0.0998605i	$-0.0318396\pi$
$468$			3.77200i			0.174361i
$469$	−9.54400			−0.440701
$470$		0			0
$471$	−17.8600			−0.822946
$472$	7.54400			0.347241
$473$			1.22800i			0.0564634i
$474$	11.5440			0.530234
$475$		−	7.77200i		−	0.356604i
$476$		−	1.00000i		−	0.0458349i
$477$	−10.5440			−0.482777
$478$	−5.22800			−0.239123
$479$		−	10.2280i		−	0.467329i	−0.972317	−	0.233665i	$-0.924928\pi$
$479$		−	10.2280i		−	0.467329i	0.972317	−	0.233665i	$-0.0750718\pi$
$480$	−1.00000			−0.0456435
$481$	14.2280	−	18.0000i	0.648741	−	0.820729i
$482$	16.0000			0.728780
$483$			7.77200i			0.353638i
$484$	10.0000			0.454545
$485$	10.7720			0.489131
$486$		−	1.00000i		−	0.0453609i
$487$			15.0880i			0.683703i	0.939754	+	0.341851i	$0.111054\pi$
$487$			15.0880i			0.683703i	−0.939754	+	0.341851i	$0.888946\pi$
$488$	12.7720			0.578161
$489$		−	3.45600i		−	0.156286i
$490$	−6.00000			−0.271052
$491$	30.2280			1.36417			0.682085	−	0.731273i	$-0.261073\pi$
$491$	30.2280			1.36417			0.682085	+	0.731273i	$0.261073\pi$
$492$	−0.772002			−0.0348045
$493$	0.772002			0.0347692
$494$			29.3160i			1.31899i
$495$			1.00000i			0.0449467i
$496$			0.772002i			0.0346639i
$497$	6.00000			0.269137
$498$			1.77200i			0.0794053i
$499$			4.68399i			0.209684i	0.994489	+	0.104842i	$0.0334337\pi$
$499$			4.68399i			0.209684i	−0.994489	+	0.104842i	$0.966566\pi$
$500$		−	1.00000i		−	0.0447214i
$501$		−	11.3160i		−	0.505562i
$502$	−27.0880			−1.20900
$503$		−	3.08801i		−	0.137687i	−0.997627	−	0.0688437i	$-0.978069\pi$
$503$		−	3.08801i		−	0.137687i	0.997627	−	0.0688437i	$-0.0219310\pi$
$504$			1.00000i			0.0445435i
$505$			11.5440i			0.513701i
$506$	7.77200			0.345508
$507$	1.22800			0.0545373
$508$	−13.3160			−0.590802
$509$	25.3160			1.12211			0.561056	−	0.827778i	$-0.310395\pi$
$509$	25.3160			1.12211			0.561056	+	0.827778i	$0.310395\pi$
$510$			1.00000i			0.0442807i
$511$	−0.227998			−0.0100860
$512$			1.00000i			0.0441942i
$513$		−	7.77200i		−	0.343142i
$514$	−4.22800			−0.186489
$515$	−17.5440			−0.773081
$516$		−	1.22800i		−	0.0540596i
$517$		0			0
$518$	3.77200	−	4.77200i	0.165732	−	0.209670i
$519$	−15.0000			−0.658427
$520$			3.77200i			0.165413i
$521$	−17.4040			−0.762484			−0.381242	−	0.924475i	$-0.624503\pi$
$521$	−17.4040			−0.762484			−0.381242	+	0.924475i	$0.624503\pi$
$522$	−0.772002			−0.0337896
$523$		−	20.0000i		−	0.874539i	−0.899331	−	0.437269i	$-0.855946\pi$
$523$		−	20.0000i		−	0.874539i	0.899331	−	0.437269i	$-0.144054\pi$
$524$			0.455996i			0.0199203i
$525$	−1.00000			−0.0436436
$526$			5.22800i			0.227952i
$527$	0.772002			0.0336289
$528$	1.00000			0.0435194
$529$	−37.4040			−1.62626
$530$	−10.5440			−0.458002
$531$			7.54400i			0.327382i
$532$			7.77200i			0.336959i
$533$			2.91199i			0.126132i
$534$	17.3160			0.749337
$535$			7.77200i			0.336013i
$536$		−	9.54400i		−	0.412238i
$537$		−	9.54400i		−	0.411854i
$538$			9.31601i			0.401642i
$539$	6.00000			0.258438
$540$		−	1.00000i		−	0.0430331i
$541$		−	11.7720i		−	0.506118i	−0.967451	−	0.253059i	$-0.918563\pi$
$541$		−	11.7720i		−	0.506118i	0.967451	−	0.253059i	$-0.0814367\pi$
$542$		−	23.0880i		−	0.991715i
$543$	−23.5440			−1.01037
$544$	1.00000			0.0428746
$545$	−7.00000			−0.299847
$546$	3.77200			0.161427
$547$			14.5440i			0.621857i	0.950433	+	0.310928i	$0.100640\pi$
$547$			14.5440i			0.621857i	−0.950433	+	0.310928i	$0.899360\pi$
$548$	19.0880			0.815399
$549$			12.7720i			0.545096i
$550$			1.00000i			0.0426401i
$551$	−6.00000			−0.255609
$552$	−7.77200			−0.330798
$553$		−	11.5440i		−	0.490901i
$554$	6.22800			0.264602
$555$	−3.77200	+	4.77200i	−0.160113	+	0.202560i
$556$	−20.3160			−0.861591
$557$		−	16.4560i		−	0.697263i	−0.937260	−	0.348631i	$-0.886646\pi$
$557$		−	16.4560i		−	0.697263i	0.937260	−	0.348631i	$-0.113354\pi$
$558$	−0.772002			−0.0326814
$559$	−4.63201			−0.195913
$560$			1.00000i			0.0422577i
$561$		−	1.00000i		−	0.0422200i
$562$	3.77200			0.159112
$563$			42.9480i			1.81004i	0.425366	+	0.905022i	$0.360145\pi$
$563$			42.9480i			1.81004i	−0.425366	+	0.905022i	$0.639855\pi$
$564$		0			0
$565$	−14.3160			−0.602279
$566$	−2.22800			−0.0936497
$567$	−1.00000			−0.0419961
$568$			6.00000i			0.251754i
$569$		−	5.31601i		−	0.222859i	−0.993772	−	0.111429i	$-0.964457\pi$
$569$		−	5.31601i		−	0.222859i	0.993772	−	0.111429i	$-0.0355429\pi$
$570$		−	7.77200i		−	0.325533i
$571$	−40.9480			−1.71362			−0.856811	−	0.515631i	$-0.827557\pi$
$571$	−40.9480			−1.71362			−0.856811	+	0.515631i	$0.827557\pi$
$572$		−	3.77200i		−	0.157715i
$573$			12.5440i			0.524033i
$574$			0.772002i			0.0322227i
$575$		−	7.77200i		−	0.324115i
$576$	−1.00000			−0.0416667
$577$		−	22.4560i		−	0.934855i	−0.884031	−	0.467428i	$-0.845181\pi$
$577$		−	22.4560i		−	0.934855i	0.884031	−	0.467428i	$-0.154819\pi$
$578$			16.0000i			0.665512i
$579$		−	6.45600i		−	0.268302i
$580$	−0.772002			−0.0320556
$581$	1.77200			0.0735150
$582$	10.7720			0.446514
$583$	10.5440			0.436688
$584$		−	0.227998i		−	0.00943463i
$585$	−3.77200			−0.155953
$586$		−	9.00000i		−	0.371787i
$587$			11.8600i			0.489515i	0.969584	+	0.244757i	$0.0787083\pi$
$587$			11.8600i			0.489515i	−0.969584	+	0.244757i	$0.921292\pi$
$588$	−6.00000			−0.247436
$589$	−6.00000			−0.247226
$590$			7.54400i			0.310582i
$591$	−11.7720			−0.484235
$592$	4.77200	+	3.77200i	0.196128	+	0.155028i
$593$	−11.5440			−0.474055			−0.237028	−	0.971503i	$-0.576173\pi$
$593$	−11.5440			−0.474055			−0.237028	+	0.971503i	$0.576173\pi$
$594$			1.00000i			0.0410305i
$595$	1.00000			0.0409960
$596$	6.00000			0.245770
$597$		−	7.54400i		−	0.308756i
$598$			29.3160i			1.19882i
$599$	−21.0880			−0.861633			−0.430816	−	0.902440i	$-0.641774\pi$
$599$	−21.0880			−0.861633			−0.430816	+	0.902440i	$0.641774\pi$
$600$		−	1.00000i		−	0.0408248i
$601$	−30.5440			−1.24592			−0.622958	−	0.782255i	$-0.714069\pi$
$601$	−30.5440			−1.24592			−0.622958	+	0.782255i	$0.714069\pi$
$602$	−1.22800			−0.0500495
$603$	9.54400			0.388662
$604$	−8.22800			−0.334792
$605$			10.0000i			0.406558i
$606$			11.5440i			0.468943i
$607$			24.0000i			0.974130i	0.873366	+	0.487065i	$0.161933\pi$
$607$			24.0000i			0.974130i	−0.873366	+	0.487065i	$0.838067\pi$
$608$	−7.77200			−0.315196
$609$			0.772002i			0.0312831i
$610$			12.7720i			0.517123i
$611$		0			0
$612$			1.00000i			0.0404226i
$613$	13.8600			0.559801			0.279900	−	0.960029i	$-0.409699\pi$
$613$	13.8600			0.559801			0.279900	+	0.960029i	$0.409699\pi$
$614$		−	28.0000i		−	1.12999i
$615$		−	0.772002i		−	0.0311301i
$616$		−	1.00000i		−	0.0402911i
$617$	16.4560			0.662493			0.331247	−	0.943544i	$-0.392531\pi$
$617$	16.4560			0.662493			0.331247	+	0.943544i	$0.392531\pi$
$618$	−17.5440			−0.705723
$619$	5.22800			0.210131			0.105065	−	0.994465i	$-0.466495\pi$
$619$	5.22800			0.210131			0.105065	+	0.994465i	$0.466495\pi$
$620$	−0.772002			−0.0310043
$621$		−	7.77200i		−	0.311880i
$622$	−6.77200			−0.271533
$623$		−	17.3160i		−	0.693751i
$624$			3.77200i			0.151001i
$625$	1.00000			0.0400000
$626$	17.0880			0.682974
$627$			7.77200i			0.310384i
$628$	−17.8600			−0.712692
$629$	3.77200	−	4.77200i	0.150400	−	0.190272i
$630$	−1.00000			−0.0398410
$631$			4.31601i			0.171817i	0.996303	+	0.0859087i	$0.0273793\pi$
$631$			4.31601i			0.171817i	−0.996303	+	0.0859087i	$0.972621\pi$
$632$	11.5440			0.459196
$633$	11.2280			0.446273
$634$		−	33.4040i		−	1.32664i
$635$		−	13.3160i		−	0.528430i
$636$	−10.5440			−0.418097
$637$			22.6320i			0.896713i
$638$	0.772002			0.0305638
$639$	−6.00000			−0.237356
$640$	−1.00000			−0.0395285
$641$	−33.8600			−1.33739			−0.668695	−	0.743537i	$-0.733147\pi$
$641$	−33.8600			−1.33739			−0.668695	+	0.743537i	$0.733147\pi$
$642$			7.77200i			0.306736i
$643$		−	13.0000i		−	0.512670i	−0.966588	−	0.256335i	$-0.917485\pi$
$643$		−	13.0000i		−	0.512670i	0.966588	−	0.256335i	$-0.0825150\pi$
$644$			7.77200i			0.306260i
$645$	1.22800			0.0483524
$646$			7.77200i			0.305785i
$647$			23.3160i			0.916647i	0.888786	+	0.458323i	$0.151550\pi$
$647$			23.3160i			0.916647i	−0.888786	+	0.458323i	$0.848450\pi$
$648$		−	1.00000i		−	0.0392837i
$649$		−	7.54400i		−	0.296128i
$650$	−3.77200			−0.147950
$651$			0.772002i			0.0302571i
$652$		−	3.45600i		−	0.135347i
$653$		−	17.0880i		−	0.668705i	−0.942448	−	0.334353i	$-0.891482\pi$
$653$		−	17.0880i		−	0.668705i	0.942448	−	0.334353i	$-0.108518\pi$
$654$	−7.00000			−0.273722
$655$	−0.455996			−0.0178172
$656$	−0.772002			−0.0301416
$657$	0.227998			0.00889505
$658$		0			0
$659$	19.0880			0.743563			0.371782	−	0.928320i	$-0.378747\pi$
$659$	19.0880			0.743563			0.371782	+	0.928320i	$0.378747\pi$
$660$			1.00000i			0.0389249i
$661$			32.0880i			1.24808i	0.781393	+	0.624039i	$0.214510\pi$
$661$			32.0880i			1.24808i	−0.781393	+	0.624039i	$0.785490\pi$
$662$	−17.5440			−0.681867
$663$	3.77200			0.146492
$664$			1.77200i			0.0687670i
$665$	−7.77200			−0.301385
$666$	−3.77200	+	4.77200i	−0.146162	+	0.184911i
$667$	−6.00000			−0.232321
$668$		−	11.3160i		−	0.437829i
$669$	17.2280			0.666073
$670$	9.54400			0.368717
$671$		−	12.7720i		−	0.493058i
$672$			1.00000i			0.0385758i
$673$	16.6840			0.643121			0.321560	−	0.946889i	$-0.395793\pi$
$673$	16.6840			0.643121			0.321560	+	0.946889i	$0.395793\pi$
$674$		−	1.31601i		−	0.0506906i
$675$	1.00000			0.0384900
$676$	1.22800			0.0472307
$677$	−27.7720			−1.06736			−0.533682	−	0.845685i	$-0.679192\pi$
$677$	−27.7720			−1.06736			−0.533682	+	0.845685i	$0.679192\pi$
$678$	−14.3160			−0.549803
$679$		−	10.7720i		−	0.413391i
$680$			1.00000i			0.0383482i
$681$			6.77200i			0.259504i
$682$	0.772002			0.0295615
$683$		−	11.6840i		−	0.447076i	−0.974695	−	0.223538i	$-0.928239\pi$
$683$		−	11.6840i		−	0.447076i	0.974695	−	0.223538i	$-0.0717606\pi$
$684$		−	7.77200i		−	0.297170i
$685$			19.0880i			0.729315i
$686$			13.0000i			0.496342i
$687$	−13.5440			−0.516736
$688$		−	1.22800i		−	0.0468170i
$689$			39.7720i			1.51519i
$690$		−	7.77200i		−	0.295875i
$691$	15.2280			0.579300			0.289650	−	0.957133i	$-0.406461\pi$
$691$	15.2280			0.579300			0.289650	+	0.957133i	$0.406461\pi$
$692$	−15.0000			−0.570214
$693$	1.00000			0.0379869
$694$	23.5440			0.893718
$695$		−	20.3160i		−	0.770630i
$696$	−0.772002			−0.0292627
$697$			0.772002i			0.0292417i
$698$		−	6.00000i		−	0.227103i
$699$	12.0000			0.453882
$700$	−1.00000			−0.0377964
$701$		−	45.5440i		−	1.72017i	−0.510148	−	0.860087i	$-0.670409\pi$
$701$		−	45.5440i		−	1.72017i	0.510148	−	0.860087i	$-0.329591\pi$
$702$	−3.77200			−0.142365
$703$	−29.3160	+	37.0880i	−1.10567	+	1.39880i
$704$	1.00000			0.0376889
$705$		0			0
$706$	36.7720			1.38393
$707$	11.5440			0.434157
$708$			7.54400i			0.283521i
$709$		−	18.5440i		−	0.696435i	−0.937414	−	0.348217i	$-0.886787\pi$
$709$		−	18.5440i		−	0.696435i	0.937414	−	0.348217i	$-0.113213\pi$
$710$	−6.00000			−0.225176
$711$			11.5440i			0.432934i
$712$	17.3160			0.648945
$713$	−6.00000			−0.224702
$714$	1.00000			0.0374241
$715$	3.77200			0.141065
$716$		−	9.54400i		−	0.356676i
$717$		−	5.22800i		−	0.195243i
$718$		−	4.45600i		−	0.166296i
$719$	−12.0000			−0.447524			−0.223762	−	0.974644i	$-0.571834\pi$
$719$	−12.0000			−0.447524			−0.223762	+	0.974644i	$0.571834\pi$
$720$		−	1.00000i		−	0.0372678i
$721$			17.5440i			0.653373i
$722$		−	41.4040i		−	1.54090i
$723$			16.0000i			0.595046i
$724$	−23.5440			−0.875006
$725$		−	0.772002i		−	0.0286714i
$726$			10.0000i			0.371135i
$727$			52.1760i			1.93510i	0.252677	+	0.967551i	$0.418689\pi$
$727$			52.1760i			1.93510i	−0.252677	+	0.967551i	$0.581311\pi$
$728$	3.77200			0.139800
$729$	1.00000			0.0370370
$730$	0.227998			0.00843859
$731$	−1.22800			−0.0454192
$732$			12.7720i			0.472067i
$733$	−13.6840			−0.505430			−0.252715	−	0.967541i	$-0.581323\pi$
$733$	−13.6840			−0.505430			−0.252715	+	0.967541i	$0.581323\pi$
$734$		−	16.0880i		−	0.593819i
$735$		−	6.00000i		−	0.221313i
$736$	−7.77200			−0.286480
$737$	−9.54400			−0.351558
$738$		−	0.772002i		−	0.0284178i
$739$	−49.8600			−1.83413			−0.917065	−	0.398738i	$-0.869448\pi$
$739$	−49.8600			−1.83413			−0.917065	+	0.398738i	$0.869448\pi$
$740$	−3.77200	+	4.77200i	−0.138662	+	0.175422i
$741$	−29.3160			−1.07695
$742$			10.5440i			0.387083i
$743$	31.8600			1.16883			0.584415	−	0.811455i	$-0.301324\pi$
$743$	31.8600			1.16883			0.584415	+	0.811455i	$0.301324\pi$
$744$	−0.772002			−0.0283030
$745$			6.00000i			0.219823i
$746$			21.5440i			0.788782i
$747$	−1.77200			−0.0648342
$748$		−	1.00000i		−	0.0365636i
$749$	7.77200			0.283983
$750$	1.00000			0.0365148
$751$	16.6320			0.606911			0.303455	−	0.952846i	$-0.401860\pi$
$751$	16.6320			0.606911			0.303455	+	0.952846i	$0.401860\pi$
$752$		0			0
$753$		−	27.0880i		−	0.987142i
$754$			2.91199i			0.106049i
$755$		−	8.22800i		−	0.299448i
$756$	−1.00000			−0.0363696
$757$			47.4920i			1.72613i	0.505096	+	0.863063i	$0.331457\pi$
$757$			47.4920i			1.72613i	−0.505096	+	0.863063i	$0.668543\pi$
$758$		−	23.5440i		−	0.855157i
$759$			7.77200i			0.282106i
$760$		−	7.77200i		−	0.281920i
$761$	40.4920			1.46783			0.733917	−	0.679239i	$-0.237690\pi$
$761$	40.4920			1.46783			0.733917	+	0.679239i	$0.237690\pi$
$762$		−	13.3160i		−	0.482388i
$763$			7.00000i			0.253417i
$764$			12.5440i			0.453826i
$765$	−1.00000			−0.0361551
$766$	−15.3160			−0.553390
$767$	28.4560			1.02749
$768$	−1.00000			−0.0360844
$769$		−	7.54400i		−	0.272044i	−0.990706	−	0.136022i	$-0.956568\pi$
$769$		−	7.54400i		−	0.272044i	0.990706	−	0.136022i	$-0.0434317\pi$
$770$	1.00000			0.0360375
$771$		−	4.22800i		−	0.152268i
$772$		−	6.45600i		−	0.232356i
$773$	33.6320			1.20966			0.604830	−	0.796355i	$-0.293241\pi$
$773$	33.6320			1.20966			0.604830	+	0.796355i	$0.293241\pi$
$774$	1.22800			0.0441395
$775$		−	0.772002i		−	0.0277311i
$776$	10.7720			0.386692
$777$	4.77200	+	3.77200i	0.171195	+	0.135320i
$778$	6.77200			0.242788
$779$		−	6.00000i		−	0.214972i
$780$	−3.77200			−0.135059
$781$	6.00000			0.214697
$782$			7.77200i			0.277926i
$783$		−	0.772002i		−	0.0275891i
$784$	−6.00000			−0.214286
$785$		−	17.8600i		−	0.637451i
$786$	−0.455996			−0.0162648
$787$	48.1760			1.71729			0.858645	−	0.512571i	$-0.171307\pi$
$787$	48.1760			1.71729			0.858645	+	0.512571i	$0.171307\pi$
$788$	−11.7720			−0.419360
$789$	−5.22800			−0.186122
$790$			11.5440i			0.410717i
$791$			14.3160i			0.509019i
$792$			1.00000i			0.0355335i
$793$	48.1760			1.71078
$794$			1.54400i			0.0547946i
$795$		−	10.5440i		−	0.373957i
$796$		−	7.54400i		−	0.267390i
$797$			27.0880i			0.959506i	0.877403	+	0.479753i	$0.159274\pi$
$797$			27.0880i			0.959506i	−0.877403	+	0.479753i	$0.840726\pi$
$798$	−7.77200			−0.275126
$799$		0			0
$800$		−	1.00000i		−	0.0353553i
$801$			17.3160i			0.611831i
$802$	23.3160			0.823317
$803$	−0.227998			−0.00804588
$804$	9.54400			0.336591
$805$	−7.77200			−0.273927
$806$			2.91199i			0.102571i
$807$	−9.31601			−0.327939
$808$			11.5440i			0.406117i
$809$		−	47.3160i		−	1.66354i	−0.555119	−	0.831771i	$-0.687327\pi$
$809$		−	47.3160i		−	1.66354i	0.555119	−	0.831771i	$-0.312673\pi$
$810$	1.00000			0.0351364
$811$	4.45600			0.156471			0.0782356	−	0.996935i	$-0.475071\pi$
$811$	4.45600			0.156471			0.0782356	+	0.996935i	$0.475071\pi$
$812$			0.772002i			0.0270920i
$813$	23.0880			0.809732
$814$	3.77200	−	4.77200i	0.132209	−	0.167259i
$815$	3.45600			0.121058
$816$			1.00000i			0.0350070i
$817$	9.54400			0.333902
$818$	4.00000			0.139857
$819$			3.77200i			0.131804i
$820$		−	0.772002i		−	0.0269595i
$821$	39.9480			1.39420			0.697098	−	0.716976i	$-0.254474\pi$
$821$	39.9480			1.39420			0.697098	+	0.716976i	$0.254474\pi$
$822$			19.0880i			0.665771i
$823$	−36.8600			−1.28486			−0.642430	−	0.766345i	$-0.722073\pi$
$823$	−36.8600			−1.28486			−0.642430	+	0.766345i	$0.722073\pi$
$824$	−17.5440			−0.611174
$825$	−1.00000			−0.0348155
$826$	7.54400			0.262489
$827$			21.6840i			0.754026i	0.926208	+	0.377013i	$0.123049\pi$
$827$			21.6840i			0.754026i	−0.926208	+	0.377013i	$0.876951\pi$
$828$		−	7.77200i		−	0.270096i
$829$			47.0000i			1.63238i	0.577785	+	0.816189i	$0.303917\pi$
$829$			47.0000i			1.63238i	−0.577785	+	0.816189i	$0.696083\pi$
$830$	−1.77200			−0.0615071
$831$			6.22800i			0.216047i
$832$			3.77200i			0.130771i
$833$			6.00000i			0.207888i
$834$		−	20.3160i		−	0.703486i
$835$	11.3160			0.391607
$836$			7.77200i			0.268800i
$837$		−	0.772002i		−	0.0266843i
$838$			12.8600i			0.444242i
$839$	14.4560			0.499076			0.249538	−	0.968365i	$-0.419721\pi$
$839$	14.4560			0.499076			0.249538	+	0.968365i	$0.419721\pi$
$840$	−1.00000			−0.0345033
$841$	28.4040			0.979449
$842$	−6.00000			−0.206774
$843$			3.77200i			0.129915i
$844$	11.2280			0.386484
$845$			1.22800i			0.0422444i
$846$		0			0
$847$	10.0000			0.343604
$848$	−10.5440			−0.362083
$849$		−	2.22800i		−	0.0764647i
$850$	−1.00000			−0.0342997
$851$	−29.3160	+	37.0880i	−1.00494	+	1.27136i
$852$	−6.00000			−0.205557
$853$			38.8600i			1.33054i	0.746602	+	0.665271i	$0.231684\pi$
$853$			38.8600i			1.33054i	−0.746602	+	0.665271i	$0.768316\pi$
$854$	12.7720			0.437049
$855$	7.77200			0.265797
$856$			7.77200i			0.265642i
$857$		−	15.0000i		−	0.512390i	−0.966625	−	0.256195i	$-0.917531\pi$
$857$		−	15.0000i		−	0.512390i	0.966625	−	0.256195i	$-0.0824690\pi$
$858$	3.77200			0.128774
$859$		−	7.77200i		−	0.265177i	−0.991171	−	0.132589i	$-0.957671\pi$
$859$		−	7.77200i		−	0.265177i	0.991171	−	0.132589i	$-0.0423289\pi$
$860$	1.22800			0.0418744
$861$	−0.772002			−0.0263098
$862$	10.0880			0.343599
$863$	32.3160			1.10005			0.550025	−	0.835148i	$-0.314618\pi$
$863$	32.3160			1.10005			0.550025	+	0.835148i	$0.314618\pi$
$864$		−	1.00000i		−	0.0340207i
$865$		−	15.0000i		−	0.510015i
$866$		−	7.77200i		−	0.264103i
$867$	−16.0000			−0.543388
$868$			0.772002i			0.0262035i
$869$		−	11.5440i		−	0.391604i
$870$		−	0.772002i		−	0.0261733i
$871$		−	36.0000i		−	1.21981i
$872$	−7.00000			−0.237050
$873$			10.7720i			0.364577i
$874$		−	60.4040i		−	2.04320i
$875$		−	1.00000i		−	0.0338062i
$876$	0.227998			0.00770334
$877$	−9.22800			−0.311607			−0.155804	−	0.987788i	$-0.549797\pi$
$877$	−9.22800			−0.311607			−0.155804	+	0.987788i	$0.549797\pi$
$878$	20.7720			0.701021
$879$	9.00000			0.303562
$880$			1.00000i			0.0337100i
$881$	−40.7720			−1.37364			−0.686822	−	0.726826i	$-0.740995\pi$
$881$	−40.7720			−1.37364			−0.686822	+	0.726826i	$0.740995\pi$
$882$		−	6.00000i		−	0.202031i
$883$			1.91199i			0.0643437i	0.999482	+	0.0321718i	$0.0102424\pi$
$883$			1.91199i			0.0643437i	−0.999482	+	0.0321718i	$0.989758\pi$
$884$	3.77200			0.126866
$885$	−7.54400			−0.253589
$886$		−	20.0000i		−	0.671913i
$887$	−27.6840			−0.929538			−0.464769	−	0.885432i	$-0.653863\pi$
$887$	−27.6840			−0.929538			−0.464769	+	0.885432i	$0.653863\pi$
$888$	−3.77200	+	4.77200i	−0.126580	+	0.160138i
$889$	−13.3160			−0.446604
$890$			17.3160i			0.580434i
$891$	−1.00000			−0.0335013
$892$	17.2280			0.576836
$893$		0			0
$894$			6.00000i			0.200670i
$895$	9.54400			0.319021
$896$			1.00000i			0.0334077i
$897$	−29.3160			−0.978833
$898$	−2.00000			−0.0667409
$899$	−0.595987			−0.0198773
$900$	1.00000			0.0333333
$901$			10.5440i			0.351272i
$902$			0.772002i			0.0257049i
$903$		−	1.22800i		−	0.0408652i
$904$	−14.3160			−0.476143
$905$		−	23.5440i		−	0.782629i
$906$		−	8.22800i		−	0.273357i
$907$		−	30.2280i		−	1.00370i	−0.864953	−	0.501852i	$-0.832652\pi$
$907$		−	30.2280i		−	1.00370i	0.864953	−	0.501852i	$-0.167348\pi$
$908$			6.77200i			0.224737i
$909$	−11.5440			−0.382890
$910$			3.77200i			0.125041i
$911$			24.0000i			0.795155i	0.917568	+	0.397578i	$0.130149\pi$
$911$			24.0000i			0.795155i	−0.917568	+	0.397578i	$0.869851\pi$
$912$		−	7.77200i		−	0.257357i
$913$	1.77200			0.0586447
$914$	−34.3160			−1.13507
$915$	−12.7720			−0.422229
$916$	−13.5440			−0.447506
$917$			0.455996i			0.0150583i
$918$	−1.00000			−0.0330049
$919$		−	32.0000i		−	1.05558i	−0.849374	−	0.527791i	$-0.823020\pi$
$919$		−	32.0000i		−	1.05558i	0.849374	−	0.527791i	$-0.176980\pi$
$920$		−	7.77200i		−	0.256235i
$921$	28.0000			0.922631
$922$	−21.2280			−0.699107
$923$			22.6320i			0.744942i
$924$	1.00000			0.0328976
$925$	−4.77200	−	3.77200i	−0.156902	−	0.124023i
$926$	30.6320			1.00663
$927$		−	17.5440i		−	0.576221i
$928$	−0.772002			−0.0253422
$929$	29.2280			0.958940			0.479470	−	0.877558i	$-0.340829\pi$
$929$	29.2280			0.958940			0.479470	+	0.877558i	$0.340829\pi$
$930$		−	0.772002i		−	0.0253149i
$931$		−	46.6320i		−	1.52830i
$932$	12.0000			0.393073
$933$		−	6.77200i		−	0.221705i
$934$	4.31601			0.141224
$935$	1.00000			0.0327035
$936$	−3.77200			−0.123292
$937$	−24.4560			−0.798943			−0.399471	−	0.916746i	$-0.630806\pi$
$937$	−24.4560			−0.798943			−0.399471	+	0.916746i	$0.630806\pi$
$938$		−	9.54400i		−	0.311623i
$939$			17.0880i			0.557646i
$940$		0			0
$941$	46.6320			1.52016			0.760080	−	0.649829i	$-0.225160\pi$
$941$	46.6320			1.52016			0.760080	+	0.649829i	$0.225160\pi$
$942$		−	17.8600i		−	0.581911i
$943$		−	6.00000i		−	0.195387i
$944$			7.54400i			0.245536i
$945$		−	1.00000i		−	0.0325300i
$946$	−1.22800			−0.0399257
$947$		−	5.86001i		−	0.190425i	−0.995457	−	0.0952124i	$-0.969647\pi$
$947$		−	5.86001i		−	0.190425i	0.995457	−	0.0952124i	$-0.0303530\pi$
$948$			11.5440i			0.374932i
$949$		−	0.860009i		−	0.0279171i
$950$	7.77200			0.252157
$951$	33.4040			1.08320
$952$	1.00000			0.0324102
$953$	25.5440			0.827451			0.413726	−	0.910402i	$-0.364227\pi$
$953$	25.5440			0.827451			0.413726	+	0.910402i	$0.364227\pi$
$954$		−	10.5440i		−	0.341375i
$955$	−12.5440			−0.405914
$956$		−	5.22800i		−	0.169086i
$957$			0.772002i			0.0249553i
$958$	10.2280			0.330452
$959$	19.0880			0.616384
$960$		−	1.00000i		−	0.0322749i
$961$	30.4040			0.980775
$962$	18.0000	+	14.2280i	0.580343	+	0.458729i
$963$	−7.77200			−0.250449
$964$			16.0000i			0.515325i
$965$	6.45600			0.207826
$966$	−7.77200			−0.250060
$967$		−	24.6320i		−	0.792112i	−0.918226	−	0.396056i	$-0.870379\pi$
$967$		−	24.6320i		−	0.792112i	0.918226	−	0.396056i	$-0.129621\pi$
$968$			10.0000i			0.321412i
$969$	−7.77200			−0.249673
$970$			10.7720i			0.345868i
$971$	−33.8600			−1.08662			−0.543310	−	0.839532i	$-0.682829\pi$
$971$	−33.8600			−1.08662			−0.543310	+	0.839532i	$0.682829\pi$
$972$	1.00000			0.0320750
$973$	−20.3160			−0.651301
$974$	−15.0880			−0.483451
$975$		−	3.77200i		−	0.120801i
$976$			12.7720i			0.408822i
$977$			33.0000i			1.05576i	0.849318	+	0.527882i	$0.177014\pi$
$977$			33.0000i			1.05576i	−0.849318	+	0.527882i	$0.822986\pi$
$978$	3.45600			0.110511
$979$		−	17.3160i		−	0.553422i
$980$		−	6.00000i		−	0.191663i
$981$		−	7.00000i		−	0.223493i
$982$			30.2280i			0.964614i
$983$	−27.4040			−0.874052			−0.437026	−	0.899449i	$-0.643968\pi$
$983$	−27.4040			−0.874052			−0.437026	+	0.899449i	$0.643968\pi$
$984$		−	0.772002i		−	0.0246105i
$985$		−	11.7720i		−	0.375087i
$986$			0.772002i			0.0245855i
$987$		0			0
$988$	−29.3160			−0.932666
$989$	9.54400			0.303482
$990$	−1.00000			−0.0317821
$991$			8.13999i			0.258575i	0.991607	+	0.129288i	$0.0412691\pi$
$991$			8.13999i			0.258575i	−0.991607	+	0.129288i	$0.958731\pi$
$992$	−0.772002			−0.0245111
$993$		−	17.5440i		−	0.556742i
$994$			6.00000i			0.190308i
$995$	7.54400			0.239161
$996$	−1.77200			−0.0561480
$997$			52.4040i			1.65965i	0.558022	+	0.829826i	$0.311560\pi$
$997$			52.4040i			1.65965i	−0.558022	+	0.829826i	$0.688440\pi$
$998$	−4.68399			−0.148269
$999$	−4.77200	−	3.77200i	−0.150979	−	0.119341i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.h.d.961.3	yes	4
3.2	odd	2		3330.2.h.j.2071.1		4
37.36	even	2	inner	1110.2.h.d.961.2	✓	4
111.110	odd	2		3330.2.h.j.2071.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.h.d.961.2	✓	4	37.36	even	2	inner
1110.2.h.d.961.3	yes	4	1.1	even	1	trivial
3330.2.h.j.2071.1		4	3.2	odd	2
3330.2.h.j.2071.4		4	111.110	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.00000i q^{6} -1.00000 q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.00000i q^{6} -1.00000 q^{7} -1.00000i q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} -3.77200i q^{13} -1.00000i q^{14} +1.00000i q^{15} +1.00000 q^{16} -1.00000i q^{17} +1.00000i q^{18} +7.77200i q^{19} +1.00000i q^{20} +1.00000 q^{21} -1.00000i q^{22} +7.77200i q^{23} +1.00000i q^{24} -1.00000 q^{25} +3.77200 q^{26} -1.00000 q^{27} +1.00000 q^{28} +0.772002i q^{29} -1.00000 q^{30} +0.772002i q^{31} +1.00000i q^{32} +1.00000 q^{33} +1.00000 q^{34} +1.00000i q^{35} -1.00000 q^{36} +(4.77200 + 3.77200i) q^{37} -7.77200 q^{38} +3.77200i q^{39} -1.00000 q^{40} -0.772002 q^{41} +1.00000i q^{42} -1.22800i q^{43} +1.00000 q^{44} -1.00000i q^{45} -7.77200 q^{46} -1.00000 q^{48} -6.00000 q^{49} -1.00000i q^{50} +1.00000i q^{51} +3.77200i q^{52} -10.5440 q^{53} -1.00000i q^{54} +1.00000i q^{55} +1.00000i q^{56} -7.77200i q^{57} -0.772002 q^{58} +7.54400i q^{59} -1.00000i q^{60} +12.7720i q^{61} -0.772002 q^{62} -1.00000 q^{63} -1.00000 q^{64} -3.77200 q^{65} +1.00000i q^{66} +9.54400 q^{67} +1.00000i q^{68} -7.77200i q^{69} -1.00000 q^{70} -6.00000 q^{71} -1.00000i q^{72} +0.227998 q^{73} +(-3.77200 + 4.77200i) q^{74} +1.00000 q^{75} -7.77200i q^{76} +1.00000 q^{77} -3.77200 q^{78} +11.5440i q^{79} -1.00000i q^{80} +1.00000 q^{81} -0.772002i q^{82} -1.77200 q^{83} -1.00000 q^{84} -1.00000 q^{85} +1.22800 q^{86} -0.772002i q^{87} +1.00000i q^{88} +17.3160i q^{89} +1.00000 q^{90} +3.77200i q^{91} -7.77200i q^{92} -0.772002i q^{93} +7.77200 q^{95} -1.00000i q^{96} +10.7720i q^{97} -6.00000i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} - 4 q^{4} - 4 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 - 4 * q^4 - 4 * q^7 + 4 * q^9	\( 4 q - 4 q^{3} - 4 q^{4} - 4 q^{7} + 4 q^{9} + 4 q^{10} - 4 q^{11} + 4 q^{12} + 4 q^{16} + 4 q^{21} - 4 q^{25} - 2 q^{26} - 4 q^{27} + 4 q^{28} - 4 q^{30} + 4 q^{33} + 4 q^{34} - 4 q^{36} + 2 q^{37} - 14 q^{38} - 4 q^{40} + 14 q^{41} + 4 q^{44} - 14 q^{46} - 4 q^{48} - 24 q^{49} - 8 q^{53} + 14 q^{58} + 14 q^{62} - 4 q^{63} - 4 q^{64} + 2 q^{65} + 4 q^{67} - 4 q^{70} - 24 q^{71} + 18 q^{73} + 2 q^{74} + 4 q^{75} + 4 q^{77} + 2 q^{78} + 4 q^{81} + 10 q^{83} - 4 q^{84} - 4 q^{85} + 22 q^{86} + 4 q^{90} + 14 q^{95} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 - 4 * q^4 - 4 * q^7 + 4 * q^9 + 4 * q^10 - 4 * q^11 + 4 * q^12 + 4 * q^16 + 4 * q^21 - 4 * q^25 - 2 * q^26 - 4 * q^27 + 4 * q^28 - 4 * q^30 + 4 * q^33 + 4 * q^34 - 4 * q^36 + 2 * q^37 - 14 * q^38 - 4 * q^40 + 14 * q^41 + 4 * q^44 - 14 * q^46 - 4 * q^48 - 24 * q^49 - 8 * q^53 + 14 * q^58 + 14 * q^62 - 4 * q^63 - 4 * q^64 + 2 * q^65 + 4 * q^67 - 4 * q^70 - 24 * q^71 + 18 * q^73 + 2 * q^74 + 4 * q^75 + 4 * q^77 + 2 * q^78 + 4 * q^81 + 10 * q^83 - 4 * q^84 - 4 * q^85 + 22 * q^86 + 4 * q^90 + 14 * q^95 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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